Problem Solving
Rearranging
Subject of formula
Substitution
Examples of application
Maths
Other Subjects
Direct Proportion
Key Objectives (Year 8)
Use formulae from mathematics and other subjects
Substitute integers into simple formulae, including examples that lead to an equation to solve
Substitute positive integers into expressions involving small powers, e.g. 3x2 + 4 or 2x3
Derive algabraic expressions and formulae
Delivery Ideas
Remember key vocabulary:
algebraic expression, equation, formula, partition, multiply out, cubed, square root, to the power of…
Show how algebra can be useful in real life.
Make clear the difference between an expression and an equation.
Use letter symbols in different ways and begin to distinguish their different roles.
For example: In the equation 4x + 3 = 47, x is a particular unknown number.
In the formula V = IR, V, I and R are variable quantities, related by the formula.
Substitution
Numbers can be substitued in place of letters. This can be the case in both expressions and equations.
If a = 4
What is the value of the expression a + 2
What is the value of the expression 6a
What is the value of the expression 6a + 2
Problem Solving
Algebra can be used to solve word problems. 1. On my last birthday I weighed 125 pounds. One year later I have put on x pounds. Which expression gives my weight one year later?
a)x 125 b) 125 + x c) x - 125 d) 125x
Rearranging the Subject of Formulae
Example:-
Rearrange to find c
a = b + c To do this we need to subtract b from both sides of the equation, giving....
a - b = c
Advanced example:-
The formula for the area of a circle is A = pr2 . Solve for r in the formula .
Formulae in Action! (Science)
the volume V of a cuboid of length l, breadth b and height h:
V = lbh
the surface area S of a cuboid with width w, depth d and height h:
S = 2dw + 2dh + 2hw
The voltage V in an electrical circuit, with current I and resistance R, is given by the formula:
V = IR
Speed = Distance ÷ Time
Density = Mass (g) ÷ Volume
Volume = Height x Length X Width
Force (N) = Mass(kg) x Acceleration(m/s2)
Amperes(current) = Volts ÷ Ohms(resistance) Useful Links
Formulae
Problem SolvingRearranging
Subject of formula
Substitution
Examples of application
- Maths
- Other Subjects
Direct ProportionKey Objectives (Year 8)
Delivery Ideas
Remember key vocabulary:
algebraic expression, equation, formula, partition, multiply out, cubed, square root, to the power of…
Show how algebra can be useful in real life.
Make clear the difference between an expression and an equation.
Use letter symbols in different ways and begin to distinguish their different roles.
For example:
In the equation 4x + 3 = 47, x is a particular unknown number.
In the formula V = IR, V, I and R
are variable quantities, related by the formula.
Substitution
Numbers can be substitued in place of letters. This can be the case in both expressions and equations.
If a = 4
What is the value of the expression a + 2
What is the value of the expression 6a
What is the value of the expression 6a + 2
Problem Solving
Algebra can be used to solve word problems.
1. On my last birthday I weighed 125 pounds. One year later I have put on x pounds. Which expression gives my weight one year later?
a) x 125 b) 125 + x c) x - 125 d) 125x
Rearranging the Subject of Formulae
Example:-
Rearrange to find c
a = b + c To do this we need to subtract b from both sides of the equation, giving....
a - b = c
Advanced example:-
The formula for the area of a circle is A = pr2 . Solve for r in the formula .
Formulae in Action! (Science)
V = lbh
S = 2dw + 2dh + 2hw
V = IR
Speed = Distance ÷ Time
Density = Mass (g) ÷ Volume
Volume = Height x Length X Width
Force (N) = Mass(kg) x Acceleration(m/s2)
Amperes(current) = Volts ÷ Ohms(resistance)
Useful Links
General help http://www.onlinemathlearning.com/algebra-help.html
Balancing equations game http://nlvm.usu.edu/en/nav/frames_asid_201_g_4_t_2.html?open=instructions&from=topic_t_2.html